Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To solve this problem, we will use the given formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass of the bottle,
- [tex]\( v \)[/tex] is the speed of the bottle.
We are given that the speed [tex]\( v \)[/tex] of the soda bottle is [tex]\( 4 \, \text{m/s} \)[/tex], and we need to calculate the kinetic energy for various masses.
### Step-by-Step Calculations
1. When the mass of the bottle is [tex]\( 0.125 \, \text{kg} \)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 0.125 \, \text{kg} \times (4 \, \text{m/s})^2 \][/tex]
[tex]\[ KE = \frac{1}{2} \times 0.125 \, \times 16 \][/tex]
[tex]\[ KE = 1.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]
2. When the mass of the bottle is [tex]\( 0.250 \, \text{kg} \)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 0.250 \, \text{kg} \times (4 \, \text{m/s})^2 \][/tex]
[tex]\[ KE = \frac{1}{2} \times 0.250 \, \times 16 \][/tex]
[tex]\[ KE = 2.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]
3. When the mass of the bottle is [tex]\( 0.375 \, \text{kg} \)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 0.375 \, \text{kg} \times (4 \, \text{m/s})^2 \][/tex]
[tex]\[ KE = \frac{1}{2} \times 0.375 \, \times 16 \][/tex]
[tex]\[ KE = 3.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]
4. When the mass of the bottle is [tex]\( 0.500 \, \text{kg} \)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 0.500 \, \text{kg} \times (4 \, \text{m/s})^2 \][/tex]
[tex]\[ KE = \frac{1}{2} \times 0.500 \, \times 16 \][/tex]
[tex]\[ KE = 4.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]
### Results Summary
- When the mass of the bottle is [tex]\( 0.125 \, \text{kg} \)[/tex], the [tex]\( KE \)[/tex] is [tex]\( 1.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \)[/tex].
- When the mass of the bottle is [tex]\( 0.250 \, \text{kg} \)[/tex], the [tex]\( KE \)[/tex] is [tex]\( 2.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \)[/tex].
- When the mass of the bottle is [tex]\( 0.375 \, \text{kg} \)[/tex], the [tex]\( KE \)[/tex] is [tex]\( 3.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \)[/tex].
- When the mass of the bottle is [tex]\( 0.500 \, \text{kg} \)[/tex], the [tex]\( KE \)[/tex] is [tex]\( 4.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \)[/tex].
By these calculations, we can observe how the kinetic energy of the bottle changes as its mass increases.
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass of the bottle,
- [tex]\( v \)[/tex] is the speed of the bottle.
We are given that the speed [tex]\( v \)[/tex] of the soda bottle is [tex]\( 4 \, \text{m/s} \)[/tex], and we need to calculate the kinetic energy for various masses.
### Step-by-Step Calculations
1. When the mass of the bottle is [tex]\( 0.125 \, \text{kg} \)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 0.125 \, \text{kg} \times (4 \, \text{m/s})^2 \][/tex]
[tex]\[ KE = \frac{1}{2} \times 0.125 \, \times 16 \][/tex]
[tex]\[ KE = 1.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]
2. When the mass of the bottle is [tex]\( 0.250 \, \text{kg} \)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 0.250 \, \text{kg} \times (4 \, \text{m/s})^2 \][/tex]
[tex]\[ KE = \frac{1}{2} \times 0.250 \, \times 16 \][/tex]
[tex]\[ KE = 2.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]
3. When the mass of the bottle is [tex]\( 0.375 \, \text{kg} \)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 0.375 \, \text{kg} \times (4 \, \text{m/s})^2 \][/tex]
[tex]\[ KE = \frac{1}{2} \times 0.375 \, \times 16 \][/tex]
[tex]\[ KE = 3.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]
4. When the mass of the bottle is [tex]\( 0.500 \, \text{kg} \)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 0.500 \, \text{kg} \times (4 \, \text{m/s})^2 \][/tex]
[tex]\[ KE = \frac{1}{2} \times 0.500 \, \times 16 \][/tex]
[tex]\[ KE = 4.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]
### Results Summary
- When the mass of the bottle is [tex]\( 0.125 \, \text{kg} \)[/tex], the [tex]\( KE \)[/tex] is [tex]\( 1.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \)[/tex].
- When the mass of the bottle is [tex]\( 0.250 \, \text{kg} \)[/tex], the [tex]\( KE \)[/tex] is [tex]\( 2.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \)[/tex].
- When the mass of the bottle is [tex]\( 0.375 \, \text{kg} \)[/tex], the [tex]\( KE \)[/tex] is [tex]\( 3.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \)[/tex].
- When the mass of the bottle is [tex]\( 0.500 \, \text{kg} \)[/tex], the [tex]\( KE \)[/tex] is [tex]\( 4.0 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \)[/tex].
By these calculations, we can observe how the kinetic energy of the bottle changes as its mass increases.
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
